The battery negative cable should NOT short to the battery tray or any other chassis parts, unless the cable ground/chassis connection is not good. The battery negative cable can touch any chassis metal with no problem, if it has a good connection to ground/chassis.
I attended a 530 car Mustang car show in Calgary over Labor Day Weekend. One of the guys in my travel group had a similar starting problem. Everything worked great with the key on. But, when he tried to start, everything went dead, no start. Turned out it was a bad cable connection. Under low load everything work normal, Under very high load, nothing. The bad connection would not handle the high amp load. When the bad connection was fixed - worked perfect.